The On-Line Encyclopedia of Bongard Problems

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Easy Bongard Problems vs. hard Bongard Problems.

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP10	BP23	BP31
BP97	BP98	BP100	BP194	BP196	BP211
BP363	BP374	BP812	BP839	BP882	BP911
BP956	BP1002	BP1015	BP1017	BP1022	BP1087
BP1095	BP1104	BP1105

BP112	BP162	BP344	BP383	BP394	BP559
BP564	BP793	BP795	BP796	BP801	BP825
BP831	BP842	BP849	BP860	BP871	BP872
BP875	BP876	BP877	BP878	BP898	BP899
BP927	BP934	BP944	BP954	BP965	BP998
BP1011	BP1038	BP1040	BP1055	BP1123	. . .

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "easy" on the OEBP.` `Right-sorted Bongard Problems have the keyword "hard" on the OEBP.` `"Easy" means easy for human beings to solve, not computers.`
	CROSSREFS	`Adjacent-numbered pages: BP496 BP497 BP498 BP499 BP500 * BP502 BP503 BP504 BP505 BP506`
	KEYWORD	`spectrum, subjective, meta (see left/right), links, keyword, sideless`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP503

"Nice" Bongard Problems vs. Bongard Problems the OEBP does not need more like.

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP11	BP12	BP15
BP16	BP20	BP23	BP30	BP32	BP33
BP50	BP51	BP57	BP59	BP62	BP70
BP71	BP72	BP74	BP76	BP77	BP85
BP97	BP98	BP100	BP106	BP108	. . .

BP213	BP214	BP221	BP231	BP237	BP262
BP538	BP545	BP548	BP555	BP570	BP801
BP862	BP882	BP915	BP920	BP941	BP1000
BP1008	BP1042	BP1043	BP1129	BP1150

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "nice" on the OEBP.` `Right-sorted Bongard Problems have the keyword "less." They are not necessarily "bad," but we do not want more like them.`
	CROSSREFS	`Adjacent-numbered pages: BP498 BP499 BP500 BP501 BP502 * BP504 BP505 BP506 BP507 BP508`
	KEYWORD	`subjective, meta (see left/right), links, keyword, oebp, right-finite, left-it, feedback, time`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP534

Bongard Problems such that potential left examples can intuitively be put in bijection with potential right examples vs. other Bongard Problems.

BP7	BP8	BP19	BP36	BP43	BP45
BP54	BP55	BP63	BP64	BP67	BP95
BP106	BP109	BP157	BP158	BP180	BP196
BP197	BP211	BP234	BP278	BP279	BP286
BP313	BP337	BP357	BP363	BP372	BP513
BP514	BP515	BP516	BP517	BP793	. . .

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	COMMENTS	`This is the keyword "dual" on the OEBP.` `Given an example there is some way to "flip sides" by altering it. The left-to-right and right-to-left transformations should be inverses.` `It is not required that there only be one such transformation. For example, for many handed Bongard Problem, flipping an example over any axis will reliably switch its sorting.` `It is not required that every left example must have its corresponding right example uploaded on the OEBP nor vice versa. See the keyword contributepairs for the BPs the OEBP advises users upload left and right examples for in pairs.`
	CROSSREFS	`Adjacent-numbered pages: BP529 BP530 BP531 BP532 BP533 * BP535 BP536 BP537 BP538 BP539`
	KEYWORD	`meta (see left/right), links, keyword, sideless`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP552

Orientation-dependent Bongard Problems vs. orientation-independent visual Bongard Problems.

BP7	BP8	BP16	BP36	BP43	BP54
BP55	BP63	BP67	BP106	BP109	BP199
BP207	BP234	BP278	BP279	BP286	BP313
BP337	BP363	BP372	BP793	BP795	BP796
BP805	BP830	BP881	BP896	BP931	BP955
BP961	BP971	BP972	BP1008	BP1014	. . .

	BP1	BP2	BP3	BP4	BP5	BP6
	BP986	BP1197	BP1199	BP1200

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	COMMENTS	`Left examples have the keyword "handed" on the OEBP.` `If mirroring any example along the any axis can change its sorting the BP is "handed."` `Note that BPs about comparing orientation between multiple things in one example fit on the right side.`
	CROSSREFS	`See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.` `The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.` `Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.` `Adjacent-numbered pages: BP547 BP548 BP549 BP550 BP551 * BP553 BP554 BP555 BP556 BP557`
	KEYWORD	`meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger] zoom in left (handed_visualbp)`
	AUTHOR	`Aaron David Fairbanks`

BP553

Rotation-dependent Bongard Problems vs. rotation-independent visual Bongard Problems.

BP7	BP19	BP36	BP65	BP95	BP106
BP152	BP158	BP199	BP273	BP523	BP551
BP971	BP1014	BP1086	BP1087	BP1213	BP1215
BP1216	BP1218	BP1245

BP16

BP54

BP1122

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	COMMENTS	`Left examples have the keyword "rotate" on the OEBP.` `If rotating an example about the center can change its sorting the BP is a left example here.` `Note that BPs about relative rotation comparisons fit on the right side.`
	CROSSREFS	`See BP872 for the version with pictures of Bongard Problems instead (miniproblems) of links to pages on the OEBP.` `Bongard Problems tagged "rotate" are usually handed, since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.` `Adjacent-numbered pages: BP548 BP549 BP550 BP551 BP552 * BP554 BP555 BP556 BP557 BP558`
	KEYWORD	`notso, meta (see left/right), links, keyword, invariance, wellfounded`
	WORLD	`visualbp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP645

Bongard Problem with solution relating to concept: horizontal vs. Bongard Problem unrelated to this concept.

BP7	BP13	BP19	BP43	BP65	BP66
BP95	BP116	BP132	BP147	BP192	BP206
BP268	BP270	BP280	BP281	BP1207

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	CROSSREFS	`Adjacent-numbered pages: BP640 BP641 BP642 BP643 BP644 * BP646 BP647 BP648 BP649 BP650`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "horizontal"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP701

Bongard Problem with solution relating to concept: slope of straight line vs. Bongard Problem unrelated to this concept.

	BP7	BP13	BP35	BP39	BP106	BP158
	BP173

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	CROSSREFS	`Adjacent-numbered pages: BP696 BP697 BP698 BP699 BP700 * BP702 BP703 BP704 BP705 BP706`
	KEYWORD	`meta (see left/right), links, metaconcept, primitive`
	CONCEPT	`This MBP is about BPs that feature concept: "line_slope"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP798

Bongard Problems by Bongard vs. other Bongard Problems.

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP10	BP11	BP12
BP13	BP14	BP15	BP16	BP17	BP18
BP19	BP20	BP21	BP22	BP23	BP24
BP25	BP26	BP27	BP28	BP29	BP30
BP31	BP32	BP33	BP34	BP35	. . .

BP101	BP102	BP103	BP104	BP105	BP106
BP107	BP108	BP109	BP110	BP111	BP112
BP113	BP114	BP115	BP116	BP117	BP118
BP119	BP120	BP121	BP122	BP123	BP124
BP125	BP126	BP127	BP128	BP129	BP130
BP131	BP132	BP133	BP134	BP135	. . .

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	COMMENTS	`Alternatively, BP pages on the OEBP with number less than or equal to 100 vs. other BP pages.` `Bongard's original Problems have the keyword "bongard" on the OEBP.`
	CROSSREFS	`Adjacent-numbered pages: BP793 BP794 BP795 BP796 BP797 * BP799 BP800 BP801 BP802 BP803`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`bppage [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP804

Bongard Problem with solution relating to concept: vertical vs. Bongard Problem unrelated to this concept.

BP7	BP13	BP19	BP65	BP66	BP95
BP116	BP132	BP147	BP192	BP206	BP268
BP270	BP280	BP281	BP1087	BP1206

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	CROSSREFS	`Adjacent-numbered pages: BP799 BP800 BP801 BP802 BP803 * BP805 BP806 BP807 BP808 BP809`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "vertical"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP983

Bongard Problem with solution relating to concept: comparison of multiple quantities (within one example) vs. Bongard Problem unrelated to this concept.

BP7	BP27	BP28	BP29	BP36	BP37
BP38	BP53	BP969	BP970	BP1208	BP1214
BP1217

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	COMMENTS	`"More," "fewer," "greater than," "less than."` `See BP752 and BP749 for equality.`
	CROSSREFS	`Adjacent-numbered pages: BP978 BP979 BP980 BP981 BP982 * BP984 BP985 BP986 BP987 BP988`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "quantity_comparison"` `Searchable synonyms: "more", "less", "greater", "lesser", "greater than", "less than", "fewer".`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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